Functionally tunable active low-pass filter

ABSTRACT

A second-order active low-pass filter in which the elements are arranged to provide a unidirectional sequence of functional tuning by varying only resistors.

United States Patent 1 1 Mikhael et al.

[ FUNCTIONALLY TUNABLE ACTIVE LOW-PASS FILTER [75] Inventors: Wasfy Boushra Mikhael, Ottawa;

Lloyd Kenneth Keys, Carp, both of Canada [73] Assignee: Northern Electric Company Limited, Montreal, Canada [22] Filed: July 19, 1974 [2|] Appl. No.: 490,108

[ June 24, 1975 OTHER PUBLlCATIONS Primary Examiner.lames B. Mullins Attorney, Agent, or F irm.lohn E. Mowle [S2] U.S. Cl 330/107; 330/3l [51] Int. Cl. l-l03F H36 57 ABSTRACT [58] Field of Search 330/2L3l, 107, 109',

2 7 A second-order active low-pass filter In whlch the elements are arranged to provide a unidirectional se- 5 References Cited quence of functional tuning by varying only resistors UNITED STATES PATENTS 2 Claims, 2 Drawing Figures 3,787,778 l/l974 Carre'et 330/l09 X 1 Gll PATENTED J UN 2 4 I975 FREQUENCY KHz Fig. 2

FUNCTIONALLY TUNABLE ACTIVE LOW-PASS FILTER This invention relates to an active low-pass filter and more particularly to one which allows a unidirectional sequence of functional tuning of attenuation, resonant frequency and quality factor by varying only resistors.

BACKGROUND OF THE INVENTION Resistive-capacitive (RC) active low-pass filters provide an economical arrangement for band-limiting signals at audio frequencies. These filters are almost always realized as a cascade of second-order sections for sensitivity and tuning considerations. R.P. Sallen and EL Key in an article entitled A Practical Method of Designing RC-Active Filters IRE Transactions-Circuit Theory, Vol. CT-2, March I955, pps 74-85, describe a number of RC-active cut-off filters for use at very low frequencies. In constructing such low-pass filters utilizing either thin or thick film techniques, it is usually nec essary to employ laser, an abrasive, or anodization trimming techniques to achieve the final filter parame ters. Consequently, it is advantageous to be able to use a unidirectional tuning sequence by trimming only re sistors. For, if the trimming elements are interdependent, it will be necessary to approach the final values in a series of ever-decreasing steps in order not to overtrim.

SUMMARY OF THE INVENTION The present invention overcomes this problem by providing an RC-active low-pass filter in which the pole resonant frequency (u the pole quality factor Q, and the d-c attenuation factor H can be tuned in a unidirectional sequence by trimming only resistors. Thus, in accordance with the present invention there is provided a functionally tunable active low-pass filter comprising a non-inverting essentially unity gain amplifier. First and second resistors are serially connected between the input of the filter and the input of the amplifier. A first capacitor is connected between the input of the amplifier and ground. A second capacitor and a third resistor are connected in shunt between the output of the amplifier and the junction of the first and second resistors. The circuit arrangement is such that only the pole quality factor 0,, is a function of the third resistor, while only the pole resonant frequency w and the pole quality factor 0,, are a function of the second resistor connected to the input of the amplifier. Thus by trimming the second and then the third resistors unidirectional functional tuning of the filter is achieved.

In order to vary the pass-band attenuation through the filter, a particular embodiment includes a fourth resistor connected between the junction of the first and second resistors and ground. Changing the value of this resistor affects the d-c attenuation factor H, the pole resonant frequency to, and the pole quality factor 0,. Hence, by trimming the fourth, second and third resistors in that order, a complete unidirectional sequence of functional tuning for an active RC low-pass filter can be readily achieved. Such a filter has relatively low sensitivity to passive element values and consequently is relatively immune to temperature and power supply variations.

BRIEF DESCRIPTION OF THE DRAWINGS An example embodiment of the invention will now be described with reference to the accompanying drawings in which:

FIG. I is a schematic circuit diagram of a functionally tunable active low-pass filter; and

FIG. 2 illustrates the frequency response ofa typical two-section filter of the type illustrated in FIG. I.

DESCRIPTION OF THE PREFERRED EMBODIMENT In the embodiment illustrated in the accompanying drawing, the passive components will be designated by reference characters, the relative values of which will be such as to satisfy the equations found in the following technical description.

Referring to FIG. 1, the functionally tunable active low-pass filter comprises an input terminal 10, an output terminal 11 and a common or ground terminal 12. A non-inverting substantially unity gain amplifier 13 has its output connected to the output terminal 11. This amplifier 13 is readily realized utilizing an operational amplifier having a high input impedance and low output impedance and by connecting its inverting input terminal to its output, as illustrated in the schematic diagram.

Connected between the input terminal I0 and the non-inverting input of the amplifier 13 are two serially connected resistors G and 0 Connected between the junction of the two resistors and the common terminal or ground 12 is a resistor G",. A capacitor C is connected between the non-inverting input of the amplifier l3 and ground. In addition, the parallel combination of a resistor G. and a capacitor C, are connected between the output of the operational amplifier l3 and the junction of the two resistors G and G As will become apparent later, the resistor G" is optional and is utilized to control the attenuation through the filter.

For an ideal operational amplifier I3, the voltage transfer ratio T(s) of this filter is as follows:

p (GI 21 4) The following is a suggested method of choosing suitable element values. In equation (I) let Using equations (2) (3) and (4) the following is derived:

Frequently, low-pass transfer function specifications require a multiplier constant different from unity. If the multiplier constant is less than or equal to unity, the cir- From equation (5), C is obtained as cuit described above can be used. For a multiplier con- 5 stant greater than unity, an additional amplifier is nor- 2 2 l/(wv R C) mally required. If this gain requirement can be incorpo- 6 rated in the filter, no additional amplifier would be required. The low-pass filter circuits of Sallen and Key From equations (4), (5) and (6), as a becomes can be designed with a d-c gain greater than unity. By

smaller, C gets larger, while G and C get small cascading the Sallen and Key circuits with those of the Unidirectional functional tuning of the filter circuit Present invemlen the advantages 0f both and low i accomplished as f ll sensitivity to element values is obtained.

First, the resistor G" is trimmed until the d-c attenu- 2 illustrates a p e p e eharaeiel'istie ation factor iS equai to (Foi- H: i 0 and this which is obtained by cascading two sections of the low- Step iS not required); pass filter illustrated in FIG. 1. Typical non-limiting resistive values of the conductive circuit components Second, an in ut si nal is a lied at a fre uenc w p 8 pp q y which are used to obtain this response are as follows:

(u and the circuit resonant frequency is adjusted by trimming resistor G until a 90 phase shift between the input terminal 10 and the output terminal 11 is ob- 2O tained; and First Section Third, the pole quality factor is adjusted by trimming $33 32? (variable) g"| 32 resistor G until the attenuation at 0),, becomes equal to 1: 40Kfl aria l C: 4:6rlF j i ri bl o" n For a single pole, frequency compensated ope a- 2 401) ya a e c3 0 2 tional amplifier 13, the open-loop gain A is given by G. g 40Kfl (variable) C l3.4nF

What is claimed is: A 2 i i (7) l. A functionally tunable active low-pass filter com- S prising:

input, output and common terminals; Where 0 and r are the g and cut-off anon-inverting essentially unity gain amplifier having q y p yits output connected to said output terminal;

Hence, the closed p gain of the essentially unity first and second resistors serially connected between gain amplifier is given by: said input terminal and the input of said amplifier; a first capacitor connected between the input of said amplifier and said common terminal; A (8) a second capacitor and a third resistor connected in .L.) shunt between the output of said amplifier and the A w A, 40 junction of said first and second resistors;

the amplifier, resistors and capacitors coacting such Using the design values given by equations (4), (6) that variations in resistance of the second resistor and considering the amplifier gain to be finite, the connected to the input of the amplifier affects only transfer function of the proposed circuit becomes the p resonant frequency p and the p q y For to, A w which is a reasonable assumption factor Q,,, and variations in resistance of the third in active filter applications, it can be shown that; resistor affects only the pole quality factor Q,,,

thereby enabling a unidirectional sequence of funcpa z (l0) tional tuning of said filter.

2. A functionally tunable active low-pass filter as deand fined in claim 1 which additionally comprises:

a fourth resistor connected between the junction of 2 Q (I i) said first and second resistors and the common teri+ minal;

the amplifier, resistors and capacitors coacting such that variations in resistance of said fourth resistor affects the d-c attenuation factor H, the pole resonant frequency w, and the pole quality factor Q where w, and Q,,,, denote the actually realized pole resonant frequency and pole quality factor respectively. 

1. A functionally tunable active low-pass filter comprising: input, output and common terminals; a non-inverting essentially unity gain amplifier having its output connected to said output terminal; first and second resistors serially connected between said input terminal and the input of said amplifier; a first capacitor connected between the input of said amplifier and said common terminal; a second capacitor and a third resistor connected in shunt between the output of said amplifier and the junction of said first and second resistors; the amplifier, resistors and capacitors coacting such that variations in resistance of the second resistor connected to the input of the amplifier affects only the pole resonant frequency omega p and the pole quality factor Qp, and variations in resistance of the third resistor affects only the pole quality factor Qp, thereby enabling a unidirectional sequence of functional tuning of said filter.
 2. A functionally tunable active low-pass filter as defined in claim 1 which additionally comprises: a fourth resistor connected between the junction of said first and second resistors and the common terminal; the amplifier, resistors and capacitors coacting such that variations in resistance of said fourth resistor affects the d-c attenuation factor H, the pole resonant frequency omega p and the pole quality factor Qp. 